Fun in the morning time entertains service staff (9)

I believe the answer is:

amusement

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'fun' is the definition.
(amusement is fun or enjoyment)

I don't understand the rest of the clue.

(Other definitions for amusement that I've seen before include "(State of) finding something funny" , "Pleasure, diversion" , "Light-hearted pastime" , "set up through arcade?" , "Fun" .)

I've seen this clue in The Times.

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